Unable to understand the second iteration update in value iteration algorithm for solving MDP
First thing to know is that, in this case, values for the gridworld in new iteration are completely calculated with respect to the old values from the previous iteration. Value of $0.78$ is got like this:  

$0.9 \cdot (0.8 \cdot 1 + 0.1 \cdot 0.72 + 0.1 \cdot 0) = 0.7848 \approx 0.78$  

term $0.8 \cdot 1$ is for going to the right with probability of $0.8$ and getting reward of $1$.  

term $0.1 \cdot 0.72$ is for going up with probability of $0.1$, we hit the wall and stay in the same field which value is $0.72$ (from previous iteration)  

term $0.1 \cdot 0$ is for going down with probability of $0.1$, even though value of that field in the image is $0.43$ we take the value from previous iteration which is $0$.